Question

solve $5x + 1 < 11$ or $-3x + 10 \leq -11$. then graph the solution set.
part a
select the solution set for $5x + 1 < 11$ or $-3x + 10 \leq -11$.
a. $\\{x|x < 2 \text{ or } x \geq 7\\}$
b. $\\{x|2 < x \leq 7\\}$
c. $\\{x|x < 2\\}$
d. $\\{x|x \leq -7 \text{ or } x > 2\\}$

Explanation:

Step1: Solve $5x + 1 < 11$

Subtract 1 from both sides:
$5x < 11 - 1$
$5x < 10$
Divide by 5:
$x < 2$

Step2: Solve $-3x + 10 \leq -11$

Subtract 10 from both sides:
$-3x \leq -11 - 10$
$-3x \leq -21$
Divide by -3 (reverse inequality):
$x \geq 7$

Step3: Combine the solutions

The compound inequality uses "or", so combine the two solution sets.

Answer:

A. $\{x|x < 2 \text{ or } x \geq 7\}$

Graphing Note (for the full problem):

• For $x < 2$: Draw an open circle at $x=2$ on a number line, shade all values to the left.
• For $x \geq 7$: Draw a closed circle at $x=7$ on the same number line, shade all values to the right.